comm.MemorylessNonlinearity

Apply memoryless nonlinearity to complex baseband signal

Description

The comm.MemorylessNonlinearity System object™ applies memoryless nonlinear impairments to a baseband signal. Use this System object to model memoryless nonlinear impairments caused by signal amplification in a radio frequency (RF) transmitter or receiver. For more information, see Memoryless Nonlinear Impairments.

To apply memoryless nonlinear impairments to a complex baseband signal:

1. Create the comm.MemorylessNonlinearity object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

mnl = comm.MemorylessNonlinearity

mnl = comm.MemorylessNonlinearity(Name=Value)

Description

mnl = comm.MemorylessNonlinearity creates a memoryless nonlinearity System object that models RF nonlinear impairments.

mnl = comm.MemorylessNonlinearity(Name=Value) specifies properties using one or more name-value pair arguments. Enclose each property name in quotes. For example, 'Method','Saleh model' sets the modeling method to the Saleh method.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Method — Nonlinearity modeling method

'Cubic polynomial' (default) | 'Hyperbolic tangent' | 'Saleh model' | 'Ghorbani model' | 'Modified Rapp model' | 'Lookup table'

Nonlinearity modeling method, specified as 'Cubic polynomial', 'Hyperbolic tangent', 'Saleh model', 'Ghorbani model', 'Modified Rapp model', or 'Lookup table'. For more information, see Memoryless Nonlinear Impairments.

Data Types: char | string

InputScaling — Input signal scaling factor

0 (default) | scalar

Input signal scaling factor in decibels, specified as a scalar. This property scales the power gain of the input signal.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Saleh model' or 'Ghorbani model'.

Data Types: double

LinearGain — Linear gain

0 (default) | scalar

Linear gain in decibels, specified as a scalar. This property scales the power gain of the output signal.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial', 'Hyperbolic tangent', or 'Modified Rapp model'.

Data Types: double

TOISpecification — Third-order nonlinearity specification for cubic polynomial

'IIP3' (default) | 'OIP3' | 'IP1dB' | 'OP1dB' | 'IPsat' | 'OPsat'

Third-order nonlinearity specification for cubic polynomial, specified as 'IIP3', 'OIP3', 'IP1dB', 'OP1dB', 'IPsat', or 'OPsat'. For more information, see Cubic Polynomial Third-Order Coefficient.

Dependencies

To enable this property, set the Method property to 'Cubic polynomial'.

Data Types: char | string

IIP3 — Third-order input intercept point

30 (default) | scalar

Third-order input intercept point in dBm, specified as a scalar.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial' or 'Hyperbolic tangent'.

Data Types: double

OIP3 — Third-order output intercept point

30 (default) | scalar

Third-order output intercept point in dBm, specified as a scalar.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial' and the TOISpecification property to 'OIP3'.

Data Types: double

IP1dB — One dB input compression point

30 (default) | scalar

One dB input compression point in dBm, specified as a scalar.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial' and the TOISpecification property to 'IP1dB'.

Data Types: double

OP1dB — One dB output compression point

30 (default) | scalar

One dB output compression point in dBm, specified as a scalar.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial' and the TOISpecification property to 'OP1dB'.

Data Types: double

IPsat — Input saturation point

30 (default) | scalar

Input saturation point in dBm, specified as a scalar.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial' and the TOISpecification property to 'IPsat'.

Data Types: double

OPsat — Output saturation point

30 (default) | scalar

Output saturation point in dBm, specified as a scalar.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial' and the TOISpecification property to 'OPsat'.

Data Types: double

AMPMConversion — Linear AM/PM conversion factor

10 (default) | scalar

Linear AM/PM conversion factor in degrees per decibel, specified as a scalar. For more information, see Cubic Polynomial and Hyperbolic Tangent Model Methods.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Cubic polynomial' or 'Hyperbolic tangent'.

Data Types: double

AMAMParameters — AM/AM parameters

[2.1587 1.1517] | [8.1081 1.5413 6.5202 -0.0718] | row vector

AM/AM parameters used to compute the amplitude gain for an input signal, specified as a row vector.

• When the Method property is set to 'Saleh model', this property must be a two-element vector that specifies alpha and beta values. In this case, the default value is [2.1587 1.1517].

• When the Method property is set to 'Ghorbani model', this property must be a four-element vector that specifies x₁, x₂, x₃, and x₄ values. In this case, the default value is [8.1081 1.5413 6.5202 -0.0718].

For more information, see Saleh Model Method and Ghorbani Model Method.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Saleh model' or 'Ghorbani model'.

Data Types: double

AMPMParameters — AM/PM parameters

[4.0033 9.1040] | [4.6645 2.0965 10.88 -0.003] | row vector

AM/PM parameters used to compute the phase change for an input signal, specified as a row vector.

• When the Method property is set to 'Saleh model', this property must be a two-element vector that specifies alpha and beta values. In this case, the default value is [4.0033 9.1040].

• When the Method property is set to 'Ghorbani model', this property must be a four-element vector that specifies y₁, y₂, y₃, and y₄ values. In this case, the default value is [4.6645 2.0965 10.88 -0.003]

For more information, see Saleh Model Method and Ghorbani Model Method.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Saleh model' or 'Ghorbani model'.

Data Types: double

PowerLowerLimit — Input power lower limit

10 (default) | scalar

Input power lower limit in dBm, specified as a scalar less than the PowerUpperLimit property value. The AM/PM conversion scales linearly for input power values in the range [PowerLowerLimit, PowerUpperLimit]. If the input signal power is below the input power lower limit, the phase shift resulting from AM/PM conversion is zero. For more information, see Cubic Polynomial and Hyperbolic Tangent Model Methods.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Cubic polynomial' or 'Hyperbolic tangent'.

Data Types: double

PowerUpperLimit — Input power upper limit

inf (default) | scalar

Input power upper limit in dBm, specified as a scalar greater than PowerLowerLimit. The AM/PM conversion scales linearly for input power values in the range [PowerLowerLimit, PowerUpperLimit]. If the input signal power is above the input power upper limit, the phase shift resulting from AM/PM conversion is constant. For more information, see Cubic Polynomial and Hyperbolic Tangent Model Methods.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Cubic polynomial' or 'Hyperbolic tangent'.

Data Types: double

OutputScaling — Output signal scaling factor

0 (default) | scalar

Output signal scaling factor in decibels, specified as a scalar. This property scales the power gain of the output signal.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Saleh model' or 'Ghorbani model'.

Data Types: double

Smoothness — Amplitude smoothness factor

0.5 (default) | scalar

Amplitude smoothness factor, specified as a scalar. For more information, see Modified Rapp Model Method.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Modified Rapp model'.

Data Types: double

PhaseGainRadian — Phase gain for modified Rapp model

0 (default) | scalar

Phase gain for modified Rapp model in radians, specified as a scalar. A value of -0.45 is typical. For more information, see Modified Rapp Model Method.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Modified Rapp model'.

Data Types: double

PhaseSaturation — Phase saturation for modified Rapp model

0.88 (default) | positive scalar

Phase saturation for modified Rapp model in radians, specified as a positive scalar. For more information, see Modified Rapp Model Method.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Modified Rapp model'.

Data Types: double

PhaseSmoothness — Phase smoothness for modified Rapp model

3.43 (default) | positive scalar | positive two-element vector

Phase smoothness for modified Rapp model in radians, specified as a positive scalar or a positive two-element vector. For more information, see Modified Rapp Model Method.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Modified Rapp model'.

Data Types: double

OutputSaturationLevel — Output saturation level

1 (default) | positive scalar

Output saturation level, specified as a scalar. For more information, see Modified Rapp Model Method.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Modified Rapp model'.

Data Types: double

Table — Amplifier characteristics lookup table

N-by-[P_in, P_out, ΔΦ] matrix

Amplifier characteristics lookup table, specified as an N-by-3 matrix of measured power amplifier (PA) characteristics. Each row is of the form [P_in, P_out, ΔΦ]. P_in specifies the input signal in dBm, P_out specifies the output signal in dBm, and ΔΦ specifies the output phase shift in degrees. The default value is [-25, 5.16, -0.25; -20, 10.11, -0.47; -15, 15.11, -0.68; -10, 20.05, -0.89; -5, 24.79, -1.22; 0, 27.64, 5.59; 5, 28.49, 12.03].

The measured PA characteristics defined by this property are used to compute the AM/AM (in dBm/dBm) and AM/PM (in deg/dBm) nonlinear impairment characteristics.

Note

To determine appropriate P_out and ΔΦ values for any P_in values below the value specified in the first row of the Table property, the System object applies the same power gain and ΔΦ as the first row, to maintain linearity and phase continuity. For any P_in higher than the value in the last row of the Table property, the System object uses linear extrapolation from last two [P_in, P_out, ΔΦ] rows of the Table.

Tunable: Yes

Dependencies

To enable this property, set the Method property to 'Lookup table'.

Data Types: double

ReferenceImpedance — Reference impedance

1 (default) | positive scalar

Reference impedance in ohms, specified as a positive scalar. This value is used to convert voltage values to power values.

Tunable: Yes

Data Types: double

Usage

Syntax

outsig = mnl(insig)

Description

outsig = mnl(insig) applies memoryless nonlinear impairments to the input RF baseband signal.

Input Arguments

insig — Input RF baseband signal

scalar | column vector | matrix

Input RF baseband signal, specified as a scalar, column vector, or matrix.

This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels. For more information, see Variable-Size Signal Support with System Objects.

Data Types: double

Output Arguments

outsig — Output RF baseband signal

scalar | column vector | matrix

Output RF baseband signal, returned as a scalar, column vector, or matrix. The output is of the same data type as the input.

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to comm.MemorylessNonlinearity

release	Release resources and allow changes to System object property values and input characteristics
clone	Create duplicate System object
isLocked	Determine if System object is in use
plot (memorylessnonlinearity)	Plot nonlinearity AM/AM and AM/PM characteristics

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Show Amplification of Signal at Linear and Nonlinear Input Power Levels

Apply cubic polynomial nonlinearity to two 16-QAM signals. The first input signal power level is in the linear region of the amplifier power characteristic curve. The second input signal power level is in the nonlinear region of the amplifier power characteristic curve. Show the amplifier power characteristic curve and the constellation diagram for the amplified 16-QAM signals.

Initialize Simulation

Initialize variables for simulation and create System objects for a memoryless nonlinearity amplifier impairment and a constellation diagram. So that the constellation shows power compression only (and no phase rotation), configure the memoryless nonlinearity amplifier impairment with AM-PM distortion set to zero.

M = 16;           % Modulation order
sps = 4;          % Samples per symbol
pindBm = [12 25]; % Input power
gain = 10;        % Amplifier gain

amplifier = comm.MemorylessNonlinearity(Method="Cubic polynomial", ...
    LinearGain=gain,AMPMConversion=0,ReferenceImpedance=50);
refConst = qammod(0:M-1,M);
axisLimits = [-gain gain];
constdiag = comm.ConstellationDiagram(NumInputPorts=2, ...
    ChannelNames=["Linear" "Nonlinear"],ShowLegend=true, ...
    ReferenceConstellation=refConst, ...
    XLimits=axisLimits,YLimits=axisLimits);

Amplify and Plot Signal

Apply 16-QAM to an input signal of random data. Amplify the signal and use the plot function of the comm.MemorylessNonlinearity System object to show the output power and phase response curves. The first input signal power level is 12 dBm and is in the linear region of the amplifier power characteristic curve. The second input signal power level is 25 dBm and is in the nonlinear region of the amplifier power characteristic curve.

pin = 10.^((pindBm-30)/10); % Convert dBm to linear Watts
data = randi([0 M-1],1000,1);
modOut = qammod(data,M,UnitAveragePower=true)*sqrt(pin*amplifier.ReferenceImpedance);
ampOut = amplifier(modOut);
plot(amplifier);

Add AWGN to the two amplified signals and show the constellation diagram for the signals.

snr = 25;
noisyLinOut = awgn(ampOut(:,1),snr,"measured");
noisyNonLinOut = awgn(ampOut(:,2),snr,"measured");
constdiag(noisyLinOut,noisyNonLinOut);

Apply Saleh Model of Power Amplifier Nonlinearity to 16-QAM Signal

Generate 16-QAM data with an average power of 10 mW and a reference impedance of 1 ohm. Pass the data through a nonlinear power amplifier (PA).

M = 16;
data = randi([0 (M - 1)]',1000,1);
avgPow = 1e-2;
minD = avgPow2MinD(avgPow,M);

Create a memoryless nonlinearity System object, specifying the Saleh model method.

saleh = comm.MemorylessNonlinearity(Method='Saleh model');

Generate modulated symbols and pass them through the PA nonlinearity model.

modData = (minD/2).*qammod(data,M);
y = saleh(modData);

Generate a scatter plot of the results.

scatterplot(y)

Average power normalization of input signal.

function minD = avgPow2MinD(avgPow,M)
    % Average power to minimum distance    
    nBits = log2(M);
    if (mod(nBits,2)==0)
        % Square QAM
        sf = (M - 1)/6;
    else
        % Cross QAM
        if (nBits>4)
            sf = ((31*M/32) - 1)/6;
        else
            sf = ((5*M/4) - 1)/6;
        end
    end
    minD = sqrt(avgPow/sf);
end

Nonlinear Amplifier Gain Compression

Plot the gain compression of a nonlinear amplifier for a 16-QAM signal.

Specify the modulation order and samples per symbol parameters.

M = 16;
sps = 4;

Model a nonlinear amplifier, by creating a memoryless nonlinearity System object with a 30 dB third-order input intercept point. Create a raised cosine transmit filter System object.

amplifier = comm.MemorylessNonlinearity(IIP3=30);
txfilter = comm.RaisedCosineTransmitFilter( ...
    RolloffFactor=0.3,FilterSpanInSymbols=6, ...
    OutputSamplesPerSymbol=sps,Gain=sqrt(sps));

Specify the input power in dBm and a reference impedance of 1 ohm. Convert the input power to W and initialize the gain vector.

pindBm = -5:25;
pin = 10.^((pindBm-30)/10);
gain = zeros(length(pindBm),1);

Execute the main processing loop, which includes these steps.

• Generate random data symbols.

• Modulate the data symbols and adjust the average power of the signal.

• Filter the modulated signal.

• Amplify the signal.

• Measure the gain.

for k = 1:length(pin)
    data = randi([0 (M - 1)],1000,1);
    modSig = qammod(data,M,UnitAveragePower=true)*sqrt(pin(k));
    filtSig = txfilter(modSig);
    ampSig = amplifier(filtSig);
    gain(k) = 10*log10(mean(abs(ampSig).^2) / mean(abs(filtSig).^2));
end

Plot the amplifier gain as a function of the input signal power. The 1 dB gain compression point occurs for an input power of 18.5 dBm. To increase the point at which a 1 dB compression is observed, increase the third-order intercept point, amplifier.IIP3.

arrayplot = dsp.ArrayPlot(PlotType='Line',XLabel='Power In (dBm)', ...
    XOffset=-5,YLimits=[-5 5]);
arrayplot(gain)

Distort 16-QAM Signal with Measured Power Amplifier Nonlinearities

Apply nonlinear power amplifier (PA) characteristics with 50 $\Omega$ impedance to a 16-QAM signal. Load PA characteristics by setting the Method property to 'Lookup table'. The pa_performance_characteristics helper function outputs the amplifier performance characteristics lookup table.

Define parameters for the modulation order, samples per symbol, and input power. Create random data.

M = 16;                     % Modulation order
sps = 4;                    % Samples per symbol
pindBm = -8;                % Input power
pin = 10.^((pindBm-30)/10); % power in Watts
data = randi([0 (M - 1)],1000,1);
refdata = 0:M-1;
refconst = qammod(refdata,M,UnitAveragePower=true);
paChar = pa_performance_characteristics();

Create a memoryless nonlinearity System object, a transmit filter System object, and a constellation diagram System object. The default lookup table values are used for the memoryless nonlinearity System object.

amplifier = comm.MemorylessNonlinearity(Method='Lookup table',Table=paChar,ReferenceImpedance=50);
txfilter = comm.RaisedCosineTransmitFilter(RolloffFactor=0.3, ...
    FilterSpanInSymbols=6,OutputSamplesPerSymbol=sps,Gain=sqrt(sps));
constellation = comm.ConstellationDiagram(SamplesPerSymbol=4, ...
    Title='Amplified/Distorted Signal',NumInputPorts=2, ...
    ReferenceConstellation=refconst,ShowLegend=true, ...
    ChannelNames={'Filtered signal','Amplified signal'});

Modulate the random data. Filter and apply the nonlinear amplifier characteristics to the modulation symbols.

modSig = qammod(data,M,UnitAveragePower=true)*sqrt(pin * amplifier.ReferenceImpedance);
filtSig = txfilter(modSig);
ampSig = amplifier(filtSig);

Compute input and output signal levels and the phase shift.

pSig = abs(ampSig).^2 / amplifier.ReferenceImpedance;
poutdBm = 10 * log10(pSig) + 30;
pfiltSig = abs(filtSig).^2 / amplifier.ReferenceImpedance;
simulated_pindBm = 10 * log10(pfiltSig) + 30;
phase = rad2deg(angle(ampSig.*conj(filtSig)));

Plot AM/AM characteristics, AM/PM characteristics, and the constellation results.

figure
set(gcf,'units','normalized','position',[.25 1/3 .5 1/3])
subplot(1,2,1)
plot(simulated_pindBm,poutdBm,'.');
hold on
plot(amplifier.Table(:,1),amplifier.Table(:,2),'.',Markersize=15);
xlabel('Input Power (dBm)')
ylabel('Output Power (dBm)');
grid on;
title('AM/AM Characteristics');
leglabel = {'Simulated results','Measurement'};
legend (leglabel,Location='south');

subplot(1,2,2)
plot(simulated_pindBm,phase,'.');
hold on
plot(amplifier.Table(:,1),amplifier.Table(:,3),'.',Markersize=15);
legend (leglabel,Location='south');
xlabel('Input Power (dBm)');
ylabel('Output Phase Shift (degrees)');
grid on;
title('AM/PM Characteristics');

For the purpose of constellation comparison, normalize the amplified signal and the filtered signal. Generate a constellation diagram of the filtered signal and amplified signal. The nonlinear amplifier characteristics cause compression of the amplified signal constellation compared to the filtered constellation.

filtSig = filtSig/mean(abs(filtSig)); % Normalized filtered signal
ampSig = ampSig/mean(abs(ampSig));    % Normalized amplified signal
constellation(filtSig,ampSig)

Helper Function

function paChar = pa_performance_characteristics()

The operating specification for the LDMOS-based Doherty amplifier are:

• A frequency of 2110 MHz

• A peak power of 300 W

• A small signal gain of 61 dB

Each row in HAV08_Table specifies Pin (dBm), gain (dB), phase shift (degrees) as derived from figure 4 of Hammi, Oualid, et al. "Power amplifiers' model assessment and memory effects intensity quantification using memoryless post-compensation technique." IEEE Transactions on Microwave Theory and Techniques 56.12 (2008): 3170-3179.

HAV08_Table =...
    [-35,60.53,0.01;
    -34,60.53,0.01;
    -33,60.53,0.08;
    -32,60.54,0.08;
    -31,60.55,0.1;
    -30,60.56,0.08;
    -29,60.57,0.14;
    -28,60.59,0.19;
    -27,60.6,0.23;
    -26,60.64,0.21;
    -25,60.69,0.28;
    -24,60.76,0.21;
    -23,60.85,0.12;
    -22,60.97,0.08;
    -21,61.12,-0.13;
    -20,61.31,-0.44;
    -19,61.52,-0.94;
    -18,61.76,-1.59;
    -17,62.01,-2.73;
    -16,62.25,-4.31;
    -15,62.47,-6.85;
    -14,62.56,-9.82;
    -13,62.47,-12.29;
    -12,62.31,-13.82;
    -11,62.2,-15.03;
    -10,62.15,-16.27;
    -9,62,-18.05;
    -8,61.53,-20.21;
    -7,60.93,-23.38;
    -6,60.2,-26.64;
    -5,59.38,-28.75];

Convert the second column of the HAV08_Table from gain to Pout for use by the memoryless nonlinearity System object.

paChar = HAV08_Table;
paChar(:,2) = paChar(:,1) + paChar(:,2);
end

More About

Memoryless Nonlinear Impairments

Memoryless nonlinear impairments distort the amplitude and phase of the input signal. The amplitude distortion is amplitude-to-amplitude modulation (AM/AM) and the phase distortion is amplitude-to-phase modulation (AM/PM). These model methods are available for simulating the memoryless nonlinear impairment models.

Model Method	Memoryless Nonlinear Impairment
Cubic polynomial	Applies AM/AM and AM/PM
Hyperbolic tangent
Saleh model
Ghorbani model
Modified Rapp model
Lookup table	Applies impairment according to [Pin, Pout, ΔΦ] amplifier characteristics specified by the Table property

The modeled impairments apply the AM/AM and AM/PM distortions differently according to the model method you specify. The models apply the memoryless nonlinear impairment to the input signal by following these steps.

1. Multiply the signal by an input gain factor.

   Note

   You can normalize the signal to 1 by setting the input scaling gain to the inverse of the input signal amplitude.

2. Split the complex signal into its magnitude and angle components. For real-valued input signals, the imaginary component is set to zero.

3. Apply an AM/AM distortion to the magnitude of the signal, according to the selected model method, to produce the magnitude of the output signal.

4. Apply an AM/PM distortion to the phase of the signal, according to the selected model method, to produce the angle of the output signal.

5. Combine the new magnitude and angle components into a complex signal. Then, multiply the result by an output gain factor.

The model methods apply AM/AM and AM/PM impairments as shown in this figure.

The lookup table method uses the power amplifier (PA) characteristics lookup table, specified as an N-by-3 matrix of measured PA characteristics. Each row is of the form [P_in, P_out, ΔΦ]. P_in specifies the PA input signal in dBm, P_out specifies the PA output signal in dBm, and ΔΦ specifies the output phase shift in degrees. The measured PA characteristics defined by the Table property are used to compute the AM/AM (in dBm/dBm) and AM/PM (in deg/dBm) nonlinear impairment characteristics. The System object distorts the input signal by the computed AM/AM (in dBm/dBm) and AM/PM (in deg/dBm) values.

Note

To determine appropriate P_out and ΔΦ values for any P_in values below the value specified in the first row of the Table property, the System object applies the same power gain and ΔΦ as the first row, to maintain linearity and phase continuity. For any P_in higher than the value in the last row of the Table property, the System object uses linear extrapolation from last two [P_in, P_out, ΔΦ] rows of the Table.

Cubic Polynomial and Hyperbolic Tangent Model Methods

This figure shows the AM/PM conversion behavior for the cubic polynomial and hyperbolic tangent model methods.

The AM/PM conversion scales linearly with an input power value between the lower and upper limits of the input power level. Outside this range, the AM/PM conversion is constant at the values corresponding to the lower and upper input power limits, which are zero and (AM/PM conversion) × (upper input power limit – lower input power limit), respectively.

Cubic Polynomial Third-Order Coefficient

The cubic polynomial model method uses linear power gain to determine the linear coefficient of a third order polynomial. The cubic polynomial model method then uses either the third order intercept point (IP3), the one dB compression point (P1dB), or the saturation power (Psat) to determine the third order coefficient of the polynomial.

This figure shows an example of the plot generated when you set the Method property to 'Cubic polynomial'.

The general form of cubic nonlinearity models the AM/AM characteristics as

$${\text{F}}_{\text{AM/AM}}{\text{(|u|)=c}}_{\text{1}}\text{×|u|+}\frac{\text{3}}{\text{4}}{\text{c}}_{\text{3}}{\text{×|u|}}^{\text{3}}$$

where FAM/AM(|u|) is the magnitude of the output signal, |u| is the magnitude of the input signal, c₁ is the coefficient of the linear gain term, and c₃ is the coefficient of the cubic gain term. The results for IIP3, OIP3, IP1dB, OP1dB, IPsat, and OPsat are taken from [6]. The coefficient c₃ values are given in this table.

Nonlinearity Type	Description	Equation
IIP3	Input power level at which the power from linear gain is equal to the power from a third-order nonlinearity	$$c_3=-\frac{4c_1}{3\times {10}^{[(IIP3-30)/10]}}$$ where IIP3 is given in dBm.
OIP3	Output power level at which the power from linear gain is equal to the power from a third-order nonlinearity	$$c_3=-\frac{4c_1^3}{3\times {10}^{[(OIP3-30)/10]}}$$ where OIP3 is given in dBm.
IP1dB	Input power level at which the output power is one dB less than the power from linear gain	$$c_3=-\frac{2c_1({10}^{\raisebox{1ex}{$19$}\!\left/ \!\raisebox{-1ex}{$20$}\right.}-10)}{15\times {10}^{[(IP1dB-30)/10]}}$$ where IP1dB is given in dBm.
OP1dB	Output power level one dB less than the power from linear gain	$$c_3=-\frac{2c_1^3({10}^{\raisebox{1ex}{$19$}\!\left/ \!\raisebox{-1ex}{$20$}\right.}-10)}{15\times {10}^{[(OP1dB-30-LGdB+1)/10]}}$$ where OP1dB is given in dBm, and LGdB is the linear gain in dB
IPsat	Input power at which the output power saturates	$$c_3=-\frac{4c_1}{9\times {10}^{[(IPsat-30)/10]}}$$ where IPsat is given in dBm.
OPsat	Output saturation power	$$c_3=-\frac{16c_1^3}{81\times {10}^{[(OPsat-30)/10]}}$$ where OPsat is given in dBm.

Saleh Model Method

This figure shows the AM/AM behavior (output voltage versus input voltage for the AM/AM distortion) and the AM/PM behavior (output phase versus input voltage for the AM/PM distortion) for the Saleh model method.

The AM/AM parameters, α_AMAM and β_AMAM, are used to compute the amplitude distortion of the input signal by using

$$F_{\text{AMAM}}(u)=\frac{{\alpha }_{\text{AMAM}}\times u}{1+{\beta }_{\text{AMAM}}\times u^2}\text{,}$$

where u is the magnitude of the scaled signal.

The AM/PM parameters, α_AMPM and β_AMPM, are used to compute the phase distortion of the input signal by using

$$F_{\text{AMPM}}(u)=\frac{{\alpha }_{\text{AMPM}}\times u^2}{1+{\beta }_{\text{AMPM}}\times u^2}\text{,}$$

where u is the magnitude of the scaled signal. The α and β parameters for AM/AM and AM/PM are similarly named but distinct.

Ghorbani Model Method

The Ghorbani model method applies AM/AM and AM/PM distortion as described in this section.

The AM/AM parameters (x₁, x₂, x₃, and x₄) are used to compute the amplitude distortion of the input signal by using

$$F_{\text{AMAM}}(u)=\frac{x_1{u}^{x_2}}{1+x_3{u}^{x_2}}+x_{4}u\text{,}$$

where u is the magnitude of the scaled signal.

The AM/PM parameters (y₁, y₂, y₃, and y₄) are used to compute the phase distortion of the input signal by using

$$F_{\text{AMPM}}(u)=\frac{y_1{u}^{y_2}}{1+y_3{u}^{y_2}}+y_{4}u\text{,}$$

where u is the magnitude of the scaled signal.

Modified Rapp Model Method

The modified Rapp model method applies AM/AM and AM/PM distortion as described in this section.

The amplitude and phase distortion of the input signal are given by:

$$F_{\text{AMAM}}(u)=\frac{g_{\text{lin}}\times u}{{\left(1+{\left(\frac{g_{\text{lin}}\times u}{O_{\text{sat}}}\right)}^{\text{2}S}\right)}^{\text{1/2}S}}\text{,}$$

$$F_{AM/PM}(u)=\frac{{\rm A}|u{|}^{q_1}}{1+{\left(\frac{\left|u\right|}{B}\right)}^{q_2}}$$

where:

• g_lin is 10^{(LinearGain/20))} and is the amplitude gain of the amplifier.

• u is the magnitude of the signal.

• S is the smoothness factor, specified by the Smoothness property.

• O_sat is the output saturation level, specified by the OutputSaturationLevel property.

• A is the phase gain in radians, specified by the PhaseGainRadian property.

• B is the phase saturation, specified by the PhaseSaturation property.

• q is the phase smoothness, specified by the PhaseSmoothness property.

  • When PhaseSmoothness property is a positive scalar value, q1 = q2 = q = PhaseSmoothness.

  • When the PhaseSmoothness property is a positive two-element vector value, q1 = PhaseSmoothness (1); q2 = PhaseSmoothness (2).

References

[1] Saleh, A.A.M. “Frequency-Independent and Frequency-Dependent Nonlinear Models of TWT Amplifiers.” IEEE^® Transactions on Communications 29, no. 11 (November 1981): 1715–20. https://doi.org/10.1109/TCOM.1981.1094911.

[2] Ghorbani, A., and M. Sheikhan. "The Effect of Solid State Power Amplifiers (SSPAs) Nonlinearities on MPSK and M-QAM Signal Transmission." In 1991 Sixth International Conference on Digital Processing of Signals in Communications (1991): 193–97.

[3] Rapp, Ch. "Effects of HPA-Nonlinearity on a 4-DPSK/OFDM-Signal for a Digital Sound Broadcasting System." In Proceedings Second European Conf. on Sat. Comm. (ESA SP-332), 179–84. Liege, Belgium, 1991. https://elib.dlr.de/33776/.

[4] Choi, C., et.al. "RF impairment models for 60 GHz-band SYS/PHY simulation." IEEE 802.15-06-0477-01-003c. November 2006.

[5] Perahia, E. "TGad Evaluation Methodology." IEEE 802.11-09/0296r16. January 20, 2010. https://mentor.ieee.org/802.11/dcn/09/11-09-0296-16-00ad-evaluation-methodology.doc.

[6] Kundert, Ken. "Accurate and Rapid Measurement of IP2 and IP3." The Designer Guide Community. May 22, 2002.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2012a

R2024b: Memory Less Nonlinearity System Object Updates

The System object now permit a 2-element phase smoothness factor with independent q₁ and q₂ values for the modified Rapp model method, as expressed in this equation.

$$F_{AM/PM}(u)=\frac{{\rm A}|u{|}^{q_1}}{1+{\left(\frac{\left|u\right|}{B}\right)}^{q_2}}$$